Question

identifying trig ratios (diagram), level 1
score: 2/10 penalty: none
question
find the value of tan c rounded to the nearest hundredth, if necessary.
answer attempt 1 out of 2
tan c =

Explanation:

Step1: Find the length of AB

Use the Pythagorean theorem \(AB=\sqrt{AC^{2}-BC^{2}}\). Given \(AC = 50\) and \(BC=14\), then \(AB=\sqrt{50^{2}-14^{2}}=\sqrt{(50 + 14)(50 - 14)}=\sqrt{64\times36}=48\).

Step2: Calculate \(\tan C\)

The formula for \(\tan\) in a right - triangle is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle C\), the opposite side is \(AB\) and the adjacent side is \(BC\). So \(\tan C=\frac{AB}{BC}\). Substitute \(AB = 48\) and \(BC = 14\), then \(\tan C=\frac{48}{14}\approx3.43\).

Answer:

\(3.43\)